A 10 Ω resistor is connected across a battery. The heat produced in the resistor per second is 40 J. The potential difference across the resistor is:

The correct answer is 20 V.

Key Points

• Given that the heat produced in the resistor per second is 40 J, this corresponds to the power dissipation in the resistor.
• The power dissipated in a resistor (P) is given by P=V2RP=V2R $P = \frac{V^2}{R}$ , where V is the potential difference and R is the resistance.
• Rearranging the formula to solve for V, we get V=P⋅R−−−−√V=P⋅R $V = \sqrt{P \cdot R}$ .
• Substituting the given values, P=40 WP=40 W $P = 40 \text{ W}$ and R=10ΩR=10Ω $R = 10 \Omega$ , into the formula, we get V=40×10−−−−−−√=400−−−√=20 VV=40×10=400=20 V $V = \sqrt{40 \times 10} = \sqrt{400} = 20 \text{ V}$ .

Additional Information

• Ohm's Law
  • It states that the current through a conductor between two points is directly proportional to the voltage across the two points.
  • The mathematical formula is V=I×RV=I×R $V = I \times R$ , where V is the voltage, I is the current, and R is the resistance.
• Joule's Law of Heating
  • It states that the heat produced in a resistor is proportional to the square of the current, the resistance, and the time for which the current flows.
  • The formula is H=I2×R×tH=I2×R×t $H = I^2 \times R \times t$ .
• Power in Electrical Circuits
  • Power (P) in an electrical circuit is given by P=V×IP=V×I $P = V \times I$ , where V is the voltage and I is the current.
  • It can also be expressed using resistance as P=V2RP=V2R $P = \frac{V^2}{R}$ or P=I2×RP=I2×R $P = I^2 \times R$ .
• Resistance
  • Resistance (R) is a measure of the opposition to current flow in an electrical circuit.
  • The unit of resistance is Ohm (Ω).
  • Resistors are used to control the current in an electrical circuit.